Probability Distributions Part I – Bernoulli, Multinoulli

Probability distributions are used in statistics to describe how likely a random variable is to take on each of it’s possible states. Random variables can be discrete and continuous.

A discrete random variable has a finite number of possible outcomes, whereas a continuous random variable has an infinite number of possible outcomes.

The Bernoulli distribution

The Bernoulli distribution deals with the probability of a binary random variable, which means that it has only two possible outcomes.

The Bernoulli distribution is controlled by one parameter , where gives the probability that the random variable will have the value 1.

Based on that, there are a couple of basic statements we can assume:

We can create an experiment using numpy.

The most applicable use of the Bernoulli distribution is a coin flip. It is used constantly in in the beginnings of sports matches. The referee flips a coin and one of the team captains needs to all heads or tails. This would assume that the coin can not fall flat on the side and stay like that forever. In sports matches, it is customary to use a coin that is “fair“, that is, it’s weight is equal on both its sides.